• Honam Mathematical Journal
• /
• v.39 no.1
• /
• pp.127-136
• /
• 2017

For a quadrangle P, we consider the centroid $G_0$ of the vertices of P, the perimeter centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P, respectively. If $G_0$ is equal to $G_1$ or $G_2$, then the quadrangle P is a parallelogram. We denote by M the intersection point of two diagonals of P. In this note, first of all, we show that if M is equal to $G_0$ or $G_2$, then the quadrangle P is a parallelogram. Next, we investigate various quadrangles whose perimeter centroid coincides with the intersection point M of diagonals. As a result, for an example, we show that among circumscribed quadrangles rhombi are the only ones whose perimeter centroid coincides with the intersection point M of diagonals.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.4
• /
• pp.429-444
• /
• 2020

For a quadrilateral P, we consider the centroid G0 of the vertices of P, the perimeter centroid G1 of the edges of P and the centroid G2 of the interior of P, respectively. It is well known that P satisfies G0 = G1 or G0 = G2 if and only if it is a parallelogram. In this paper, we investigate various quadrilaterals satisfying G1 = G2. As a result, we establish some characterization theorems. One of them asserts the existence of convex quadrilaterals satisfying G1 = G2 without symmetry.

• Honam Mathematical Journal
• /
• v.39 no.3
• /
• pp.431-442
• /
• 2017

For a quadrilateral P, we consider the centroid $G_0$ of the vertices of P, the perimeter centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P, respectively. We denote by M the intersection point of two diagonals of P. If P is a parallelogram, then we have $G_0=G_1=G_2=M$. Conversely, one of $G_0=M$ and $G_2=M$ implies that P is a parallelogram. In this paper, we show that $G_1=M$ is also a characteristic property of parallelograms.

• Honam Mathematical Journal
• /
• v.39 no.2
• /
• pp.247-258
• /
• 2017

For a quadrilateral P, we consider the centroid $G_0$ of the vertices of P, the perimeter centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P, respectively. It is well known that P satisfies $G_0=G_1$ or $G_0=G_2$ if and only if it is a parallelogram. In this note, we investigate various quadrilaterals satisfying $G_1=G_2$. As a result, for example, we show that among circumscribed quadrilaterals kites are the only ones satisfying $G_1=G_2$. Furthermore, such kites are completely classified.

• Communications of the Korean Mathematical Society
• /
• v.32 no.1
• /
• pp.135-145
• /
• 2017

For a polygon P, we consider the centroid $G_0$ of the vertices of P, the centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P. When P is a triangle, (1) we always have $G_0=G_2$ and (2) P satisfies $G_1=G_2$ if and only if it is equilateral. For a quadrangle P, one of $G_0=G_2$ and $G_0=G_1$ implies that P is a parallelogram. In this paper, we investigate the relationships between centroids of quadrangles. As a result, we establish some characterizations for rhombi and show that among convex quadrangles whose two diagonals are perpendicular to each other, rhombi and kites are the only ones satisfying $G_1=G_2$. Furthermore, we completely classify such quadrangles.

• Communications of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.709-714
• /
• 2017

For every interval [a, b], we denote by (${\bar{x}}_A,{\bar{y}}_A$) and (${\bar{x}}_L,{\bar{y}}_L$) the geometric centroid of the area under a catenary y = k cosh((x - c)/k) defined on this interval and the centroid of the curve itself, respectively. Then, it is well-known that ${\bar{x}}_L={\bar{x}}_A$ and ${\bar{y}}_L=2{\bar{y}}_A$. In this paper, we show that one of ${\bar{x}}_L={\bar{x}}_A$ and ${\bar{y}}_L=2{\bar{y}}_A$ characterizes the family of catenaries among nonconstant $C^2$ functions. Furthermore, we show that among nonconstant and nonlinear $C^2$ functions, ${\bar{y}}_L/{\bar{x}}_L=2{\bar{y}}_A/{\bar{x}}_A$ is also a characteristic property of catenaries.

• Communications of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.237-245
• /
• 2018

For every interval [a, b], we denote by $({\bar{x}}_A,{\bar{y}}_A)$ and $({\bar{x}}_L,{\bar{y}}_L)$ the geometric centroid of the area under a catenary curve y = k cosh((x-c)/k) defined on this interval and the centroid of the curve itself, respectively. Then, it is well-known that ${\bar{x}}_L={\bar{x}}_A$ and ${\bar{y}}_L=2{\bar{y}}_A$. In this paper, we fix an end point, say 0, and we show that one of ${\bar{x}}_L={\bar{x}}_A$ and ${\bar{y}}_L=2{\bar{y}}_A$ for every interval with an end point 0 characterizes the family of catenaries among nonconstant $C^2$ functions.

• Fisheries and Aquatic Sciences
• /
• v.4 no.1
• /
• pp.1-9
• /
• 2001

This paper describes a procedure extracting feature vector of a target cell more precisely in the case of identifying specified cell. The classification of object type is based on feature vector such as area, complexity, centroid, rotation angle, effective diameter, perimeter, width and height of the object So, the feature vector plays very important role in classifying objects. Because the feature vectors is affected by noises and holes, it is necessary to remove noises contaminated in original image to get feature vector extraction exactly. In this paper, we propose the following method to do to get feature vector extraction exactly. First, by Otsu's optimal threshold selection method and morphological filters such as cleaning, filling and opening filters, we separate objects from background an get rid of isolated particles. After the labeling step by 4-adjacent neighborhood, the labeled image is filtered by the area filter. From this area-filtered image, feature vector such as area, complexity, centroid, rotation angle, effective diameter, the perimeter based on chain code and the width and height based on rotation matrix are extracted. To prove the effectiveness, the proposed method is applied for yeast Zygosaccharomyces rouxn. It is also shown that the experimental results from the proposed method is more efficient in measuring feature vectors than from only Otsu's optimal threshold detection method.

• Journal of Biosystems Engineering
• /
• v.19 no.4
• /
• pp.380-396
• /
• 1994

A personal computer based color machine vision system with video camera and fluorescent lighting system was used to generate images of stationary tobacco leaves. Image processing algorithms were developed to extract both the geometric and the color features of tobacco leaves. Geometric features include area, perimeter, centroid, roundness and complex ratio. Color calibration scheme was developed to convert measured pixel values to the standard color unit using both statistics and artificial neural network algorithm. Improved back propagation algorithm showed less sum of square errors than multiple linear regression. Color features provide not only quality evaluation quantities but the accurate color measurement. Those quality features would be useful in grading tobacco automatically. This system would also be useful in measuring visual features of other agricultural products.

• Journal of Biosystems Engineering
• /
• v.17 no.2
• /
• pp.143-155
• /
• 1992

The aim of this study is to develop a general purpose algorithm for analyzing geometrical features of agricultural products and microscopic particles regardless of their numbers, shapes and positions with a computer vision system. Primarily, boundary informations of an image were obtained by Scan Line Coding and Scan & Chain Coding methods and then with these informations, geometrical features such as area, perimeter, lengths, widths, centroid, major and minor axes, equivalent circle diameter, number of individual objects, etc, were analyzed. The algorithms developed in this study was evaluated with test images consisting of a number of randomly generated ellipsoids or a few synthesized diagrams having different features. The result was successful in terms of accuracy.